The Kézaco of the episode 2.02:
It appears 2 little seconds just in front of the Chrysler 300 of Murray, and makes me think more or less to the rear of a 1994-98 2nd generation Ford Scorpio, but:
- neither the 1st gen. 4-door sedan nor this model were sold in the USA (Merkur Scorpio);
- it's clearly not the same trunk:

The 1986-90 Mercury Sable don't fit either (wrong plate place and inadequate C-pilar):

Any idea ?(I checked the "around 90" GM "Elrivado", so as the Oldsmobile Cutlass Ciera, the Taurus and even the European 4-door Ford Sierra. Nope. I'm sure I know this car. Really frustrating )

Episode 2.03: the action take place mostly indoors, so there is not a lot of car scenes. 2 Kézakos, this time:(00:01:39 // 00:07:14 - 2 different cars. And of course, no better shot, for maximum pleasure )

Episode 2.07:
[...]Does anyone have an idea of what "512" is made from? Maybe is it already identified in another movie or TV-series?

Answer to myself: not already identified, but it's for sure a Ford F-350, as it is (or is supposed to be) a FDNY vehicle. The side mirror looks like a 1999-2007 MY one.
Maybe a front view in another episode / TV-series will help to identify more precisely the MY.

Episode 2.10: once again, most of the action takes place indoor. Street views are mostly used as intros for new scenes and vehicles are just background ones, so there is not a lot of new cars to see, except:

- a 2008-2012 Chevrolet Malibu and a 2006–2009 Ford Fusion:(00:00:19 // 00:22:46 - )
Seen twice : at the beginning, and 22 minutes later, as the episode "reboots" after 1 minute with a "2 days earlier" note.

Episode 2.10: once again, most of the action takes place indoor. Street views are mostly used as intros for new scenes and vehicles are just background ones, so there is not a lot of new cars to see, except:

(00:32:11 - )

- an unknown blurry truck:

(00:32:12 to 00:32:13 - )

That looks like GM based truck. I can't tell if this is Chevrolet or GMC

That looks like GM based truck. I can't tell if this is Chevrolet or GMC

@Edit: I see the GMC grille here

Thanks for the hint, rjluna2! I think I found our "winner":

It's a third generation (2003-2009) GMC TopKick crew cab.
And it is most probably belonging to the LIRR, when you look at the logo on the door (first and second pictures of the truck).
________

Off-topic: Cadillac One, Obama's presidential limousine, use the same chassis and driveline as this truck. No wonder why some nicknamed it "The Beast" (if present in IMCDb, what is the name given to presidential limo? Just "Cadillac DTS"?)

Episode 2.13 (season finale): a murder during "Scary Carrie" high school reunion.
All the action takes place in the hotel of the meeting, in the Major Crimes unit office or, when in Carrie's memory, in the high school halls or inside a house during a party. There is only one short outdoor scene (00:22:56 - 00:23:22) without noticeable (or non-blurry) vehicles, and 2 transitional scenes with passing vehicles and a stuck BMW E66:(00:05:58 // 00:05:59 - - Supposed to be the evening, during the reunion)

(00:34:16 // 00:34:17 - - The "next day". But the BMW is exactly at the same place )

The only car really visible more than 1 second in this episode (so the Crown Victoria is disqualified ) is this "paralyzed" 2002-2005 BMW 7 Series E66 (= with long wheelbase) in a transitional scene. I don't think this is worth a particular page...
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For the record, I just noticed that the order for the episodes I saw was slightly different from the "official" one. Don't ask me why.
So, here is the "translation" of "my" episodes:
(Fr ⇒ Us)
2.01 - 2.07 ⇒ no mess
2.08 ⇒ 2.10
2.09 ⇒ 2.11
2.10 ⇒ 2.08
2.11 ⇒ 2.12
2.12 ⇒ 2.09
2.13 is Ok.
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As I don't know when I'll have the opportunity to watch the 3rd season, I hand over to anyone who wants...

Ok, let's handle the 3rd season. 13 episodes broadcast between June 29, 2014 and September 14, 2014.
This time I'll publish these episodes in the correct order (i.e. the one given by the IMDb), even if not the one of the French broadcast
_____

Background vehicles :
• Shown less than 1 second in a slide show on Jay's screens, to illustrate the actions of an Indonesian terrorist group:(00:15:49 - )
Known as 1991-98 Mazda 121 on many markets. Was it sold in the USA?

• 1989-2001 International 4000-Series:(00:30:54 - )
Most probably a 1989-94 model, in fact, as it doesn't seem to have the 1995+ hood side emblem.

Some other background vehicles have already appeared during scene transitions in the 2nd season:

• Already seen in in episode 2.10, a 2000-06 Chevrolet Suburban:(00:19:31 - )

• The 2003-09 GMC TopKick also seen in the same episode (2.10):(00:19:32 - )
As Chevrolet and GMC models can both have this grille, it was identified as a GMC truck by rjluna2 2 years ago thanks to the blurry slightly visible and possibly red logo on the grille. But the red top line in the hood side emblem indicates indeed (clearly) a GMC truck.
_____

Some are new ones in new scene transitions:

• A 1993?-2001 Freightliner FL-Series:(00:29:28 - )

• Some other vehicles, including a 1997-2002 Ford E-Series:(00:29:30 - )

• I thought this SUV was already identified, but I can't find it again. Do anyone have an idea of what it is?(00:32:47 - )